Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H...
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Transcript of Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H...
![Page 1: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/1.jpg)
Sebastian Enriquez
![Page 2: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/2.jpg)
Square Parallelogram & Rectangle: B*HTriangle: ½ B*HTrapezoid: ½ (B1+B2)HKite & Rhombus: ½(D1)(D2)
3
5
Area=15
5
5Area=25
25
3
Area=75
![Page 3: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/3.jpg)
Basically a composite figure is that which is made up of two or more different figures (ex: square and triangle). To find the area of a composite figure you find the area of each shape individually and then add up the area of the two shapes.
![Page 4: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/4.jpg)
10
20
3
5
Total Area: 207.5
10
5 8
Total Area= 158.5
27
3540
Total Area= 2990
![Page 5: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/5.jpg)
Finding the are of a circle is a simple task you only have to use the formula πr^2
24
Area=12 π or 452
36
Area= 36 π or 4071
40
Area= 40 π or 5026
![Page 6: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/6.jpg)
A solid is a 3D figure which can be made up of flat or round faces. The flat face in a solid is known as a face, the segment which intersects two faces is known as the edge and point where three or more faces intersect is the vertex.
![Page 7: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/7.jpg)
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![Page 8: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/8.jpg)
A prism is a solid which has two end faces which are similar, equal and parallel and that has sides which are parallelograms. A net is how the faces of a prism are organized so that when you connect them you get the 3D figure. To find the Surface Area of a prism you need to do Perimeter x Height + 2B.
To find the volume of a prism you need the volume of the prism x Height.
![Page 9: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/9.jpg)
2πr^2+2πr(H) is the formula used to find the surface area of a cylinder.
To find the volume of a cylinder you need this formula: πr^2(H)
![Page 10: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/10.jpg)
25
10
Surface Area= 2198
Volume= 7853
6
9 Surface Area= 847
Volume= 1526
12
6 Surface Area= 678
Volume= 1357
![Page 11: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/11.jpg)
To find the surface area of a pyramid you have to use the following formula: (base area) + ½ (Perimeter) x slant length.A pyramid is a three dimensional figure where all the faces except for the base are triangles and converge at one point known as the apex.
Volume of a pyramid is equal to: 1/3Area of the base x Height
![Page 12: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/12.jpg)
Surface Area= 261
Volume= 33
8 8
12.33
2.2
3.1
Surface Area= 19
Volume=3
30
26
Surface Area= 390
Volume=260
![Page 13: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/13.jpg)
To find the surface area of a cone you have to find the area of the cone π r s and the surface area of the base which is πr^2, then the whole formula is πrs+ πr^2.
To find the volume of a cone you need to do: 1/3(Area of Base)(Height)= 1/3πr^2h
![Page 14: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/14.jpg)
6
15Surface Area= 395
Volume= 565
3.5
5.6Surface Area= 100
Volume=72
7
12 Surface Area= 263
Volume= 615
![Page 15: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/15.jpg)
To find the volume of a cube you multiply width*length*height.
Width= 25
Height=25
Length=25
Volume=15625
Width= 33
Height=33
Length=33
Volume=35937
Width= 1.5Height=1.5Length=1.5Volume=3.375
![Page 16: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/16.jpg)
Cavalieri’s principle states that if two regions in a solid are parallel and there’s any planes that are parallel and intersect both regions, then the two regions have equal volume.
![Page 17: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/17.jpg)
15 cm
15 cm
They have the same height therefore they’re equal
![Page 18: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/18.jpg)
To find the surface area of spheres you need to do: 4π(r^2)
To find the volume of a sphere you need to do: 4/3π (r^3)
![Page 19: Sebastian Enriquez. Square Parallelogram & Rectangle: B*H Triangle: ½ B*H Trapezoid: ½ (B1+B2)H Kite & Rhombus: ½(D1)(D2) 3 5 Area= 15 5 5Area =25 25.](https://reader036.fdocuments.net/reader036/viewer/2022062309/56649f135503460f94c272b9/html5/thumbnails/19.jpg)
5
Surface Area= 314
Volume= 500
8
Surface Area= 804
Volume= 2048
8
Surface Area= 201
Volume=256